For starters, the EU and U.K. have to negotiate what they're going to negotiate. The U.K. wants to set up a trade deal with the EU while working out the fine details of the exit. But some EU representatives want to focus on Brexit and save the trade deal for later.

Then there's the relationship between the two estranged powers. Two particularly contentious issues might arise: access to the EU's single market and the movement of EU citizens between countries.

Until negotiations are finished, the U.K. will still be a part of the EU. That means the country still gets the economic benefits of membership, but it also means it can't formally work out trade deals on its own with other non-EU countries until it leaves.